Publication detail

Goertzel Algorithm Generalized to Non-integer Multiples of Fundamental Frequency

SYSEL, P. RAJMIC, P.

Original Title

Goertzel Algorithm Generalized to Non-integer Multiples of Fundamental Frequency

English Title

Goertzel Algorithm Generalized to Non-integer Multiples of Fundamental Frequency

Type

journal article in Web of Science

Language

en

Original Abstract

The paper deals with the Goertzel algorithm, used to establish the modulus and phase of harmonic components of a signal. The advantages of the Goertzel approach over the DFT and the FFT in cases of a few harmonics of interest are highlighted, with the paper providing deeper and more accurate analysis than can be found in the literature, including the memory complexity. But the main emphasis is placed on the generalization of the Goertzel algorithm, which allows us to use it also for frequencies which are not integer multiples of the fundamental frequency. Such an algorithm is derived at the cost of negligibly increasing the computational and memory complexity.

English abstract

The paper deals with the Goertzel algorithm, used to establish the modulus and phase of harmonic components of a signal. The advantages of the Goertzel approach over the DFT and the FFT in cases of a few harmonics of interest are highlighted, with the paper providing deeper and more accurate analysis than can be found in the literature, including the memory complexity. But the main emphasis is placed on the generalization of the Goertzel algorithm, which allows us to use it also for frequencies which are not integer multiples of the fundamental frequency. Such an algorithm is derived at the cost of negligibly increasing the computational and memory complexity.

Keywords

Goertzel algorithm, generalization, spectrum, DFT, DTFT, DTMF

RIV year

2012

Released

22.03.2012

Publisher

SpringerOpen

ISBN

1687-6172

Periodical

EURASIP Journal on Advances in Signal Processing

Year of study

2012

Number

1

State

US

Pages from

1

Pages to

20

Pages count

20

URL

Full text in the Digital Library

Documents

BibTex


@article{BUT89671,
  author="Petr {Sysel} and Pavel {Rajmic}",
  title="Goertzel Algorithm Generalized to Non-integer Multiples of Fundamental Frequency",
  annote="The paper deals with the Goertzel algorithm, used to establish the modulus and phase of harmonic components of a signal. The advantages of the Goertzel approach over the DFT and the FFT in cases of a few harmonics of interest are highlighted, with the paper providing deeper and more accurate analysis than can be found in the literature, including the memory complexity. But the main emphasis is placed on the generalization of the Goertzel algorithm, which allows us to use it also for frequencies which are not integer multiples of the fundamental frequency. Such an algorithm is derived at the cost of negligibly increasing the computational and memory complexity.",
  address="SpringerOpen",
  chapter="89671",
  doi="10.1186/1687-6180-2012-56",
  institution="SpringerOpen",
  number="1",
  volume="2012",
  year="2012",
  month="march",
  pages="1--20",
  publisher="SpringerOpen",
  type="journal article in Web of Science"
}